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I was wondering whether there is some accepted graphical way of reporting and inspecting sphericity, i.e. visualizing the pairwise differences and their variances (other than looking at the var-covariance matrix itself)?

I skimmed my textbooks and papers at hand, but found no hints obvious to me. What am I missing?

Thx for your pointers!

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I suggest computing new variables for m-1 normalized orthogonal contrasts among m measures. If sphericity is met then, in the population, the m-1 variables should be indepedent and have equal variance. A scatterplot matrix showing a scatterplot for each pair of contrasts should be helpful.

Note the assumption as stated here is the same as the one you refer to, but is a bit easier to visualize and is easier to generalize to, say, 3 way interactions.

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  • $\begingroup$ Hi David, thx for the suggestion (hadn't thought about that). My humble approach right now is to compute the differences between pairs of factor combinations and to plot them as a combined box- and dotplot. What do you think? $\endgroup$
    – mrcalvin
    Commented Mar 6, 2017 at 11:02
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    $\begingroup$ That makes sense but what I like about my suggestion is that it reveals the consequential aspect of violating sphericity: correlations among contrasts. You might want to take a look at this: tqmp.org/RegularArticles/vol12-2/p114/p114.pdf $\endgroup$
    – David Lane
    Commented Mar 6, 2017 at 15:08
  • $\begingroup$ An excellent write-up, very informative! The best overview on notions of sphericity plus recommendations I have personally come across so far. $\endgroup$
    – mrcalvin
    Commented Mar 7, 2017 at 16:46

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